# Infocom 2009 : routing

Scalable Routing Via Greedy Embedding
Cedric Westphal (Docomo Labs USA, US); Guanhong Pei (Virginia Tech, US)
In a network, a greedy routing strategy that sends packets to the neighbor closest to the destination may require routing tables of size $O(n)$. What we would like is to embed the network into (Euclidean or other) space in such a way that greedy routing requires only knowlege of your own location and your neighbor’s locations. The dimension needed may be as high as $O(\log n)$, but embedded graph may not be faithful to the true network, resulting in longer paths than greedy routing on the true network. This paper presents a practical distributed algorithm for embedding a graph with $n$ vertices into $\mathbb{R}^{\log n}$ with greedy forwarding. It works by extracting a spanning tree from the network and then using random projections on the label space to go from dimension $n$ to dimension $\log n$, using the popular results of Achlioptas. The tree structure serves as a backbone to avoid too much backtracking. The main point seems to be that the algorithm can be implemented in a distributed manner, but I was not clear on how this would be done.

Greedy Routing with Bounded Stretch
Roland Flury (ETH Zurich, Switzerland); Sriram Pemmaraju (The University of Iowa, US); Roger Wattenhofer (ETH Zurich, Switzerland)
This was another talk about greedy routing. If the network has holes in it (imagine a lake) then greedy routing can get stuck because there is no greedy step to take. So there are lots of algorithms out there for recovering when you are stuck. It would be far nicer to get a coordinate system for the graph such that greedy routing always works (in some sense), but so that the stretch is not too bad. This talk proposed a scheme which had three ingredients: spanning trees, separators, and isometric greedy embeddings. Basically the idea (from what I saw in the talk) is to use the existence of separators in the graph to build a tree cover of the graph and then do routing along the best tree in the cover. This guarantees the bounded stretch, and the number of trees needed is not too large, so the labels are not too large either. I think it was a rather nice paper, and between the previous one and this one I was introduced to a new problem I had not thought about before.

Routing Over Multi-hop Wireless Networks with Non-ergodic Mobility
Chris Milling (The University of Texas at Austin, US); Sundar Subramanian (Qualcomm Flarion Technologies, US); Sanjay Shakkottai (The University of Texas at Austin, US); Randall Berry (Northwestern University, US)
In this paper they had a network with some static nodes and some mobile nodes who move in prescribed areas but with no real “model” on their motion. They move arbitrarily according to some arbitrary continuous paths. Some static nodes need to route packets to the mobile nodes. How should they do this? A scheme is proposed in which the static node sends out probe packets to iteratively quarter the network and corral the mobile node. If the mobile crosses a boundary then a node close to the boundary will deliver the packet. An upperbound on the throughput can be shown by considering the mobiles to be at fixed locations (chosen to be the worst possible). This is essentially the worst case, since the rates achieved by their scheme are within a polylog factor of the upper bound. This suggests that the lack of knowledge of the user’s mobility patterns hurts very little in the scaling sense.